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lv TARLE I. - Tangents and Externals.to a 1° Curve. <br />Chord --100 ft. <br />Int. <br />Angle <br />Tangent <br />External <br />l <br />Ange <br />Tangent External <br />Int. <br />Angle <br />Tangent <br />External <br />48° <br />22Z77.0 <br />428.5 <br />50° <br />2671.8 <br />592.3 <br />57° <br />3110.9 <br />796,1 <br />10' <br />2266.6 <br />432.0 <br />10' <br />2681,9 <br />596.6 <br />10' <br />3121.7 <br />795.2 <br />20 <br />2276.2 <br />435.6 <br />20 <br />2692.1 <br />600.9 <br />20 <br />3132.6 <br />800.4 <br />30 <br />2285.9 <br />439.2 <br />30 <br />2702.3 <br />605.3 <br />30 <br />3143.4 <br />605.6 <br />40 <br />2205.6 <br />442.8 <br />40 <br />2712.5 <br />609.6 <br />40 <br />3154.2 <br />810.9 <br />50 <br />2305.2 <br />446.4 <br />50 <br />2722.7 <br />614.0 <br />50 <br />3165.1 <br />816.1 <br />44 <br />2314.9 <br />450.0 <br />51 <br />2732.9 <br />618.4 <br />58 <br />3176.0 <br />821.4 <br />10 <br />2324,6 <br />453.6 <br />10 <br />2743.1 <br />622.8 <br />10 <br />3186.9 <br />826.7 <br />20 <br />2334.3 <br />457.3 <br />20 <br />2753.4 <br />627.2 <br />20 <br />3197.8 <br />832.0 <br />30 <br />2344,1 <br />461.0 <br />30 <br />2763.7 <br />631.7 <br />30 <br />3208.8 <br />837.3 <br />40 <br />2353:8 <br />464.6 <br />40 <br />2773.9 <br />636,2 <br />40 <br />3219.7 <br />842.7 <br />60 <br />2303.5 <br />468.4 <br />50 <br />2784.2 <br />640.7 <br />50 <br />3230.7 <br />848.1 <br />46 <br />2373.3 <br />472.1 <br />52 <br />2794.5 <br />646.2 <br />69 <br />3241.7 <br />853.5 <br />10 <br />2383.1 <br />475.8 <br />10 <br />2804.9 <br />649.7 <br />10 <br />3252.7 <br />858.9 <br />20 <br />2392.8 <br />479.6 <br />20 <br />2815.2 <br />654.3 <br />20 <br />3263.7 <br />804.3 <br />30 <br />2402.5 <br />483.4 <br />30 <br />2825.6 <br />658.8 <br />30 <br />3274.8 <br />809.8 <br />40 <br />2412.4 <br />487.2 <br />40 <br />2835.0 <br />663.4 <br />40 <br />3285.8 <br />875.3 <br />50 <br />2422.3 <br />491.0 <br />50 <br />2846.3 <br />668.0 <br />50 <br />3296.0 <br />880.8 <br />46 <br />2432.1 <br />494.8 <br />53 <br />2856,7 <br />672.7 <br />60 <br />3308.0 <br />886.4 <br />10 <br />2441.9 <br />498.7 <br />10 <br />2867.1 <br />677.3 <br />10 <br />3319.1 <br />892.0 <br />20 <br />30 <br />2451.8 <br />2461.7 <br />502.5 <br />20 <br />2877.5 <br />682.0 <br />20 <br />3330.3 <br />897.5 <br />40 <br />2471.5 <br />506.4 <br />510.3 <br />30 <br />40 <br />2888.0 <br />2898.4 <br />686.7 <br />691.4 <br />30 <br />40 <br />3341.4 <br />3352,6 <br />903.2 <br />905.8 <br />50 <br />2481.4 <br />514.3 <br />50 <br />2908.9 <br />696.1 <br />50 <br />3363.8 <br />914.5 <br />67 <br />2491.3 <br />518.2 <br />54 <br />2919.4 <br />700,9 <br />61 <br />3375.0 <br />920.2 <br />10 <br />2501.2 <br />522,2 <br />10 <br />2929.9 <br />705.7 <br />10 <br />3386.3 <br />925.9 <br />20 <br />2511.2 <br />526.1 <br />20 <br />2940.4 <br />710.5 <br />20 <br />3397.5 <br />931.6 <br />30 <br />2521.1 <br />530,1 <br />30 <br />2951.0 <br />715.3 <br />30 <br />3408.8 <br />937.3 <br />40 <br />2531.1 <br />534,2 <br />40 <br />2961.5 <br />720.1 <br />40 <br />3420.1 <br />943.1 <br />50 <br />2541.0 <br />538.2 <br />50 <br />29T2.1 <br />725.0 <br />50 <br />3431.4 <br />948.9 <br />48 <br />2551.0 <br />542.2 <br />55 <br />2982.7 <br />729.9 <br />62 <br />3442.7 <br />954.8 <br />10 <br />2561.0 <br />546.3 <br />10 <br />2993,3 <br />734.8 <br />10 <br />3454.1 <br />900.6 <br />20 <br />2571.0 <br />550.4 <br />20 <br />3003,9 <br />739.7 <br />20 <br />3465.4 <br />960.5 <br />30 <br />2581.0 <br />554.5 <br />30 <br />3014,5 <br />744.6 <br />30 <br />3476,8 <br />972.4 <br />40 <br />259E 0 <br />558.6 <br />40 <br />3025:2 <br />749.6 <br />40 <br />3488.3 <br />978.3 <br />50 <br />2601.1 <br />562.8 <br />50 <br />3035.8 <br />754.6 <br />50 <br />3499.7 <br />984.3 <br />40 <br />2611.2 <br />566.9 <br />56 <br />3046.5 <br />759.6 <br />63 <br />3511.1 <br />990.2 <br />10 <br />2621.2 <br />571.1 <br />10 <br />3057.2 <br />704.6 <br />10 <br />3522.6 <br />996.2 <br />20 <br />2631.3 <br />575.3 <br />20 <br />3007.9 <br />709.7 <br />20 <br />3534.1 <br />1002.3 <br />30 . <br />2641.4 <br />579.5 <br />30 <br />3078.7 <br />774.7 <br />30 <br />3545.6 <br />1008.3 <br />40 <br />2651.5 <br />583.8 <br />40 <br />3089.4 <br />779.8 <br />40 <br />3557.2 <br />1014.4 <br />50 <br />2661.6 <br />588.0 <br />50 <br />3100.2 <br />784.9 <br />50 <br />3568.7 <br />1020.5 <br />Corrections to be Added (T =Tangent. E=External.) <br />Anglo <br />Angle <br />Curve 5° to, <br />l5° 20° 25° <br />39° 35° 40° 45° SO 55° 60° 65° 70° <br />4D° <br />TA.13 .28 <br />.40 .53 .67 <br />.80 .93 .106 1.20 1.34 1.49 1.64 1.79 1.94 <br />External <br />E=,023 .040 <br />.070 .093 .117 <br />.141 .172 .203 .234 .265 ,277 290 .315 .341 <br />45° <br />T=.16 .30 <br />.44 .60 .76 <br />.01 1.06 1.21 1.37 1.52 1.70 1.87 2.04 221 <br />4639.8 <br />E=,030 .060 <br />.093 .119 .153 <br />.184 ,216 .254 .289 .325 .33I .378 .411 .445 <br />50° <br />T=-17 .34 <br />.51 .68 .85 <br />1.02 1.19 1.36 1.54 1.72 1.91 2.10 2.20 2.48 <br />10' <br />-E-.037 .076 <br />.116 .151 .189 <br />.227 .266 .305 .345 384 .425 .467 .508 .550 <br />55° <br />T=.19 .38 <br />.57 .76 .95 <br />1.14 112 1.52 1.72 1.92 2.24 2.35 2.50 2.77 <br />1322.9 <br />E=,046 093 <br />�T=.21 <br />.142 .188 .238 <br />.283 .332 3.81 .420 .479 .530 .582 .841 .709 <br />30 <br />.42 <br />.63 .84 1.05 <br />1.27 1.49 1.71 1.94 2.17 2.38 2.60 2.83 3,07 <br />4124.8 <br />E_ <br />=.056. .112 <br />.108 .225 .283 <br />.340 .457 <br />�o <br />T=.23 ' .48 <br />$ m.067 <br />.69 .93 1.16 <br />.398 .516 .575 .636 .697 .774 .851 <br />1.40 1.04 1.88 2.13 2_38 2.63 2.88 3.13 3.39 <br />40 <br />.135 <br />.204 .273 343 <br />.412 .483 .554 .625 .697 .711 .845 .922 1.01 <br />TABLE I. -- Tangents and Externals to a 1' Curve, V <br />Chord =100 ft. <br />Int. <br />' Angle <br />Tangent <br />External <br />Int. <br />Angle <br />Tangent <br />External <br />Int' <br />`Angle <br />Tangent <br />g <br />External <br />64° <br />3580.3 <br />1026.6 <br />711 <br />4086.9 <br />1308.2 <br />78° <br />4639.8 <br />1643.0 <br />10' <br />3591.9 <br />1032.8 <br />10' <br />4099.5 <br />1315.6 <br />10' <br />4G53.6 <br />1651.7 <br />20 <br />3603.5 <br />1039.0 <br />20 <br />4112.1 <br />1322.9 <br />20 <br />4667.4 <br />1660.5 <br />30 <br />3615.1 <br />1045.2 <br />30 <br />4124.8 <br />1330.3 <br />30 <br />4681.3 <br />1669.2 <br />40 <br />3626.8 <br />-1051.4 <br />40 <br />4137.4 <br />1337.7 <br />40 <br />4605.2 <br />1678.1 <br />50 <br />3038.5 <br />1057.7 <br />50 <br />4150.1 <br />1245.1 <br />50 <br />4709.2 <br />1686.9 <br />65 <br />3650.2 <br />1063.9 <br />72 <br />41G2.8 <br />1352.6 <br />79 <br />4723.2 <br />1695.8 <br />10 <br />3661.9 <br />1070.2 <br />10 <br />4175.6 <br />1360.1 <br />10 <br />4737.2 <br />1704.7 <br />20 <br />3673.7 <br />1076.6 <br />20 <br />4188.5 <br />1367.6 <br />20 <br />4751.2 <br />1713.7 <br />30 <br />3685.4 <br />1082.9 <br />30 <br />4201.2 <br />1375.2 <br />30 <br />4765.3 <br />1722.7 <br />40 <br />3697.2 <br />1089.3 <br />40 <br />4214.0 <br />1382.8 <br />40 <br />4779.4 <br />1731.7 <br />50 <br />3709.0 <br />1095.7 <br />50 <br />4226.8 <br />1390.4 <br />50 <br />4793.6 <br />1740.8 <br />66 <br />3720.9 <br />1102.2 <br />73 <br />4230.7 <br />1398.0 <br />80 <br />4807.7 <br />1749.9 <br />10 <br />3732.7 <br />1108.6 <br />10 <br />4252.6 <br />1405.7 <br />10 <br />4822.0 <br />1759.0 <br />20 <br />3744.6 <br />1115.1 <br />20 <br />4265.6 <br />1413.5 <br />20 <br />4836.2 <br />1768,2 <br />30 <br />3756.5 <br />1121.7 <br />30 <br />4278.5 <br />1421.2 <br />30 <br />4850.5 <br />1777.4 <br />40 <br />3768.5 <br />1128.2 <br />40 <br />4291.5 <br />1429.0 <br />40 <br />4804.8 <br />1786.7 <br />50 <br />3780.4 <br />1134.8 <br />50 <br />4304.6 <br />1436.6 <br />50 <br />4879.2 <br />1796.0 <br />67 <br />3792.4 <br />1141.4 <br />74 <br />4311.6 <br />1444.6 <br />61 <br />4893.6 <br />1805.8 <br />10 <br />3804.4 <br />1148.0 <br />LO <br />4330.7 <br />1452.5 <br />10 <br />4908.0 <br />1814.7 <br />20 <br />•3816.4 <br />1154.7 <br />20 <br />4343.8 <br />1460.4 <br />20 <br />4922.5 <br />1824.1 <br />30 <br />3828.4 <br />1161.3 <br />30 <br />4350.9 <br />1468.4 <br />30 <br />4937.0 <br />1833.6 <br />40 <br />3840.5 <br />1168.1 <br />40 <br />4370.1 <br />1476.4 <br />40 <br />4951.5 <br />1843.1 <br />50 <br />3852.6 <br />1174.8 <br />50 <br />4383.3 <br />1484.4 <br />50 <br />4966;1 <br />1852.6 <br />68 <br />3864.7 <br />11SL 6 <br />76 <br />4396.5 <br />1492.4 <br />82 <br />4980.7 <br />1862.2 <br />10 <br />3876.8 <br />1188.4 <br />10 <br />4409.8 <br />1500.5 <br />10 <br />4995:4 <br />1871.8 <br />20 <br />3889.0 <br />1195.2 <br />20 <br />4423.1 <br />1508.6 <br />20 <br />5010.0 <br />1881.5 <br />30 <br />3901.2 <br />1202.0 <br />30 <br />4436.4 <br />1516.7 <br />30 <br />5024.8 <br />1891.2 <br />40 <br />3913.4 <br />1208.9 <br />40 <br />4449.7 <br />1524.9 <br />40 <br />5039.5 <br />1900.0 <br />50 <br />3925.6 <br />1215.8 <br />50 <br />4463.1 <br />1533.1 <br />50 <br />5054.3 <br />1910.7 <br />69 <br />3937.0 <br />12227 <br />76 <br />4476.5 <br />1541.4 <br />83 <br />5069.2 <br />1920.5 <br />10 <br />3950.2 <br />1229.7 <br />10 <br />4489.9 <br />1549.7 <br />10 <br />5084.0 <br />1.930.4 <br />20 <br />3962.5 <br />1236.7 <br />20 <br />4503.4 <br />1558.0 <br />20 <br />5099.0 <br />1940.3 <br />30 <br />3974.8 <br />1243.7 <br />30 <br />4516.9 <br />1560.3 <br />30 <br />5113.9 <br />1950.3 <br />40 <br />3987.2 <br />1250.8 <br />40 <br />4530.4 <br />1574.7 <br />40 <br />5128.9 <br />1960.2 <br />50 <br />3999.5 <br />1257.9 <br />50 <br />4544.0 <br />1583.1 <br />50 <br />5143.9 <br />1970.3 <br />70 <br />4011.9 <br />1265.0 <br />77 <br />4551.6 <br />1591.6 <br />84 <br />5159.0 <br />1080.4 <br />10 <br />4024.4 <br />1272.1 <br />LO <br />4571.2 <br />1600.1 <br />10 <br />5174.1 <br />1990.5 <br />20 <br />4036.8 <br />1279.3 <br />20 <br />4584.8 <br />1608.6 <br />20 <br />5189.3 <br />2000.6 <br />30 <br />4619.3 <br />1286.5 <br />30 <br />4598.5 <br />1617.1 <br />30 <br />5204.4 <br />2010.8 <br />40 <br />4061.8 <br />1293.6 <br />40 <br />4612.2 <br />1625.7 <br />40 <br />5219.7 <br />2021.1 <br />50 <br />4074.4 <br />1300.9 <br />50 <br />4626.0 <br />1634.4 <br />50 <br />5234.9 <br />2031.4 <br />Corrections to be Added (T = Tangent. E -= External.) <br />Int. <br />Curve S° <br />10° <br />1S° <br />20° 1 35° <br />40° 45° 50° <br />SS° 60° 65° 70°T=.21 <br />.42 <br />.63 <br />.84 1.49 <br />1.71 1.94 2.17 <br />2.38 2.60 2.88 3.07 <br />E =.058 <br />.712 <br />.168 <br />.225 .398 <br />.457 .516 .575 <br />.036 .697 ,774 .851 <br />65' <br />T=.23 <br />.46 <br />69 <br />125-30- <br />D3 1.64 <br />1.88 2.13 2.38 <br />2.63 2.88 8.18 8.88 <br />E=.067 <br />.135 <br />.201 <br />.273 .483 <br />.654 .625 .697 <br />.711 .845 .922 1.01 <br />70° <br />T=.25 <br />.61 <br />76 <br />1.02 1.80 <br />2.08 2.33 2.60 <br />2.88 '3.16 8.44 8.72 <br />E =.080 <br />.159 <br />.240 <br />.3215 .568 <br />.052 .735 .819 <br />.ODO .994 1.08 1.17 <br />75° <br />T=.27 <br />.55 <br />.83 <br />1.12 1.40 1.69 1.98 <br />2.27 2.57 2.87 <br />3.16 3.47 8.78 COD <br />E=.095 <br />.182 <br />.286 <br />.383 .480 .578 .678 <br />.777 .877 .977 <br />1.07 1.18 1.29 1.39 <br />$0° <br />=.30 <br />.61 <br />91 <br />1.22 1.53 1.84 2.15 <br />2.48 2.78 3.10 <br />3.44 3.78 4.12 4.46 <br />_ <br />E =.110 <br />.220 <br />332 <br />.445 .558 .671 .787 <br />.9031.02 1.13 <br />1.25 1.38 1.50 1.62_ <br />85° <br />T=-33 <br />66 <br />1.00 <br />1.33 L.68 2.02 2.36 <br />2.70 3.05 3.40 <br />3.77 4.14 4.68 2.89 <br />E =,128 <br />.259 .391 <br />.524 .657 .790 .926 <br />1.08 11.20 1.34 <br />1.47 1.82 1.78 1:91 <br />